800score.com http://www.800score.com/forum/ 

GMAT Permutations http://www.800score.com/forum/viewtopic.php?f=3&t=11168 
Page 1 of 1 
Author:  Robert.Delane [ Wed Oct 31, 2012 6:10 pm ] 
Post subject:  GMAT Permutations 
Find the number of distinguishable permutations for the letters. a) DOODLE b) DECEMBER  Hi, I am in the GMAT prep course. I am learning permutations right now but got stuck on these two problems of permutations with repetitions. I don't know how the answers came out the way they did. 
Author:  Gennadiy [ Wed Oct 31, 2012 6:37 pm ] 
Post subject:  Re: GMAT Permutations 
Quote: Hi, I am in the GMAT prep course. I am learning permutations right now but got stuck on these two problems of permutations with repetitions. I don't know how the answers came out the way they did. Let's solve the "a) DOODLE" problem first.Imagine that all the letters in the word "DOODLE" are different. For example, let's color them. DOODLE Calculating the number of permutations of 6 different objects is simple: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 The following "words" are among these permutations DDLEOO DDLEOO But if the letters "D" were not colored, then this "words" would be just one word: DDLEOO So each word with not colored D corresponds to 2 words with colored D. And instead of 6! variants we will get 6!/2 = 720/2 = 360 . Now, if we decolour "O" as well, we will get 6!/(2 × 2) = 180 variants. This solution should help you understand where the denominator in the formula n!/(s1! × s2! × ...) comes from. Don't forget that we have factorials in the denominator. In the second problem, "b) DECEMBER", the letter "E" is given three times. The rest of the letters appear only once. So the formula we use is 8! / 3! = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1) = 6720 One decolourized variant EEEDCMBR corresponds to 3! = 6 colorized variants (as if all the objects were different): EEEDCMBR EEEDCMBR EEEDCMBR EEEDCMBR EEEDCMBR EEEDCMBR Remember, you do not need to colourize and decolourize objects each time, but understanding how the formula works will help you to remember it and use appropriately. 
Page 1 of 1  All times are UTC  5 hours [ DST ] 
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/ 